I used Idemitsu type HK (SP-III) in both the power steering and the transmission.
The PSF-4 has an operating viscosity around 7.5cst, but is full synthetic. ATF +4 or Dexron-III should also work in the power steering application.
ATF +4 has more friction modifier than SP-III, while Dexron-III has less friction modifier than SP-III. The consensus for ATF+4 is in transmission use is unclear, but it should be a much closer match than the Valvoline maxlife (around 5.8-6.0 Cst)
EDIT: The role of friction modifiers in ATF seems to be commonly misunderstood. Friction modifiers reduce, not increase, the coefficient of friction between the clutch discs. This is especially important for cars that use a "partial lockup" torque converter, which requires slippage to occur within the TCC. If this slippage cannot occur, the computer senses this error and will attempt to disengage and re-engage the TCC. This phenomena is commonly referred to as "torque converter shudder" and can damage or destroy a torque converter clutch.
The disadvantage of friction modifier is that it makes the rest of the clutches "slippery" as well, increasing engagement time and potentially increasing wear.
Transmission engineers, when designing a fluid/gearbox, must find a good middle ground between too much and too little friction modifiers.